🧮 algebra

1. **Problema 4a: Resolució del sistema lineal pel mètode de Gauss** Tenim el sistema:

1. **State the problem:** We are given that $y$ varies directly with $x$ and the constant of variation is $\frac{2}{3}$. We need to find the value of $x$ when $y=18$.

1. **State the problem:** Evaluate the expression $3 \times 10 + 8 - 4^2$. 2. **Recall the order of operations:** Use PEMDAS (Parentheses, Exponents, Multiplication and Division fr

1. **State the problem:** Simplify the expression $3 \times 10 - 8 - 4^2$. 2. **Recall order of operations:** According to PEMDAS/BODMAS, calculate exponents first, then multiplica

1. **State the problem:** We have a rectangular pool where the length is three times the width. The perimeter of the pool is 32 metres. We need to find the length and width. 2. **D

1. **State the problem:** Simplify the expression $$\frac{10x - 5}{2x - 1} \times 10$$. 2. **Rewrite the expression:** The multiplication by 10 can be written as multiplication by

1. **State the problem:** Simplify the expression $(-5)^2 - 2 \times (-9) + 6$. 2. **Recall the rules:**

1. The problem is to determine the correct placement of the number 2 in an expression involving brackets. 2. When a number is outside the brackets, it usually means multiplication

1. **State the problem:** Simplify the expression $$\frac{6 - 18x}{2} \times \frac{5}{1 - 3x}$$. 2. **Rewrite the expression:**

1. **State the problem:** Solve the equation $6x - 2x = 32$ for $x$. 2. **Combine like terms:** Since both terms on the left side have $x$, subtract the coefficients:

1. **State the problem:** Factor the expression $$16x^2y^8 - 4$$. 2. **Identify common factors:** Both terms have a common factor of 4.

1. **State the problem:** Given the equation $x^2 + y^2 = 1$, show that $$\frac{\frac{x}{y}}{1 + \frac{y^2}{x^2}} = xy.$$\n\n2. **Rewrite the expression:** The left side is a compl

1. The problem asks to simplify the expression $$\frac{x}{y}$$ given the context of question 23. 2. Since the user message includes multiple expressions but requests to solve quest

1. The problem is to solve the equation shown in the screenshot (assuming it is a quadratic equation or similar). Since the image is not accessible, please provide the equation tex

1. The problem asks to solve parts a and d of a given question, but since the exact question is not provided, I will demonstrate how to solve a typical algebraic problem for part a

1. **Problem Statement:** Martina's pension contributions follow a ratio of 3:3:1 for employee, employer, and State respectively, totaling €1351 in the first year. We need to find

1. **Problem:** Write an equation in slope-intercept form of the line that passes through the point (1, 3) and is parallel to the graph of the equation $y = 3x + 2$. 2. **Recall:**

1. **State the problem:** Eleven's garden is rectangular with an area of 240 square feet. The length and width are consecutive even numbers. We need to find the perimeter of the ga

1. Plantegem el problema: Resoldre el sistema lineal per el mètode de Gauss: $$\begin{cases} x + 2y - z = 0 \\ 2x - y + z = -1 \\ -x + y + z = 6 \end{cases}$$

1. **State the problem:** Find the value of $x$ when the area of the rectangle is 10 cm². 2. **Formula for area of a rectangle:**

1. **State the problem:** Simplify the expression $2(3a+4b)-(8a-b)$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside.